Color table compression

ABSTRACT

In some examples, a print cartridge includes a memory device comprising quantized coefficients derived from a compression of a difference table including a plurality of difference nodes in which each difference node represents a value that is a difference of a value of a node of a color table and a value of a corresponding node of a reference table, the quantized coefficients useable to produce a reconstructed difference table, and a plurality of residue nodes in which each residue node represents a value that is a difference of a value of a node of the color table and a value of a corresponding node of the reconstructed difference table.

CROSS REFERENCE TO RELATED APPLICATIONS

This is a continuation of International Application No.PCT/US2016/060873, filed Nov. 7, 2016, which claims priority fromInternational Application No. PCT/US2016/041633, filed Jul. 8, 2016,which are both hereby incorporated by reference in their entirety.

BACKGROUND

Color management systems deliver a controlled conversion between colorrepresentations of various devices, such as image scanner, digitalcamera, computer monitors, printers, and corresponding media. Deviceprofiles provide color management systems with information to convertcolor data between color spaces such as between native device colorspaces and device-independent color spaces, between device-independentcolor spaces and native device color spaces, and between source devicecolor spaces and directly to target device color spaces.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram illustrating an example memory device having acompressed color table.

FIG. 2 is a block diagram illustrating an example method of compressingthe color table for the memory device of FIG. 1.

FIG. 3 is a block diagram illustrating an example method havingadditional features of the example method of FIG. 2.

FIG. 4 is a block diagram illustrating another example memory devicehaving compressed color table.

FIG. 5 is a block diagram illustrating an example method of decoding acompressed color table.

FIG. 6 is a block diagram illustrating an example system incorporatingexamples of the methods of FIGS. 2, 3 and 4 and the memory devices ofFIGS. 1 and 4.

FIG. 7 is a block diagram illustrating an example system incorporatingexamples of the methods of FIG. 5 and memory devices of FIGS. 1 and 2.

DETAILED DESCRIPTION

In the following detailed description, reference is made to theaccompanying drawings, which form a part hereof, and in which are shownby way of illustration as specific examples in which the disclosure maybe practiced. It is to be understood that other examples may be utilizedand structural or logical changes may be made without departing from thescope of the present disclosure. The following detailed description,therefore, is not to be taken in a limiting sense, and the scope of thepresent disclosure is defined by the appended claims. It is to beunderstood that features of the various examples described herein may becombined, in part or whole, with each other, unless specifically notedotherwise.

A color space is a system having axes and that describes colornumerically. Some output devices, such as two-dimensional andthree-dimensional (additive manufacturing) printing devices, may employa type of cyan-magenta-yellow-key (black) (CMYK) color space, while somesoftware applications and display devices may employ a type ofred-green-blue (RGB) color space. Additionally, some software devicesmay employ a monochromatic or gray scale color space. For example, acolor represented in the CMYK color space has a cyan value, a magentavalue, a yellow value, and a key value that combined numericallyrepresent the color.

Color tables that provide transformations between various color spacesare extensively used in color management, common examples being thetransformations from device independent color spaces (such as CIELAB,i.e., L*a*b*) to device dependent color spaces (such as RGB or CMYK) andvice versa. The mappings may be specified using tables such as one ormore single or multidimensional lookup tables, to which interpolationcan be applied, or through a series of parameters for transformations. Acolor table can include an array or other data structure on a memorydevice that replaces runtime computations with a simpler array indexingoperation as a color lookup table. For the purposes of this disclosure,color tables can also include monochromatic and gray scale color tables.

For example, a color table can include a set of M nodes that mayaccommodate M colors from a range of total colors. Each node includes aparticular color value represented as a set of bits or bytes. A colortable of 256 colors in the RGB color space may be represented with 256nodes with each node having a depth of 18 bits, i.e., six bits for eachvalue of red, green, and blue.

A color profile is a data file that characterizes the transformationbetween different color spaces. In one example, a color profile candescribe the color attributes of a particular device or viewingspecifications with a mapping between the device-dependent color space,such as a source or target color space, and a device-independent colorspace, such as profile connection space (PCS), and vice versa. Devicesand software programs—including printers, monitors, televisions,operating systems, browsers, and other device and software—that captureor display color can include profiles that comprise various combinationsof hardware and programming.

An ICC profile is an example color profile that is a set of data thatcharacterizes a color space according to standards promulgated by theInternational Color Consortium (ICC). The ICC profile framework has beenused as a standard to communicate and interchange between various colorspaces. An ICC profile includes a number of data records that can varywith the type of device. Some records, such as those including colorlookup tables, provide data for use in color transformations. A colorlookup table record includes multiple components that provide parametersfor color transformations between device space and the PCS. The lookuptables can include color conversion matrices, one-dimensional lookuptables, and multidimensional lookup tables. The number of channels atthe input and the output of the lookup table will vary depending on thecolor space involved.

ICC profiles are often embedded in color documents as variouscombinations of hardware and programming to achieve color fidelitybetween different devices, which increases the total size of thesedocuments. Each graphical element, i.e. a figure or image in the colordocument may have its own ICC profile. The size of color tables in thecolor profiles will also increase with finer sampling of the spaces andlarger bit depths. For devices such as color printers, the color tablesare often embedded in the printer firmware or other hardware, where thecolor tables consume computer memory in storage devices.

In general, a profile can include N color tables to be processed, suchas CLUT₁, CLUT₂, . . . , CLUT_(N). Multiple color tables representingdifferent rendering intents are often be included with one ICC profile.Further, the input color space includes J_(in) channels and the outputcolor space includes J_(out) channels, and in many examples of an ICCprofile J_(in) and J_(out) can be one or more channels. For each outputchannel, the corresponding lookup table contains M^(J) ^(in) nodes.

In some scenarios, the amount of firmware memory consumed for storingthese color tables can become a concern, particularly as the number ofthe look up tables in color devices increases to support multiple colorspaces, print media, and preferences. The trend toward finer sampling ofthe spaces and larger bit depths also results in an increase in tablesizes, further exacerbating these memory concerns. Additionally, theconcerns of efficient memory use and storage space consumption areapplicable for color tables that are embedded in color documents such asICC source profiles. In applications in which embedded profiles areused, the embedded profiles represent an overhead.

FIG. 1 illustrates an example memory device 100 including a compressedcolor table 102. The compressed color table 102 may be a compressedoriginal color table. The original color table includes a set of nodes.In one example, the memory device 100 can be included on a printercartridge or printer. In another example, the memory device 100 isincluded in cooperating parts, such as one part on a printer cartridgeand another part on the printer that can be processed together. Thecompressed color table 102 is provided on the memory device 100 asincluding a compressed difference table 104 and a residue table 106. Thecompressed color table 102 can be stored as a set of files, includingbinary files, or as bitstreams. The difference table 104 includes aplurality of difference nodes in which each node represents a differencebetween a value of a node of an original color table and a value of anode of a reference table. The reference table includes nodes having apreselected, or predetermined value. In one example, the values of thenodes of the reference table are representative of the nodes of theoriginal color table. The residue table 106 includes a plurality ofresidue nodes in which each node represents a difference of between avalue of a node of the original color table and a value of a node of areconstructed compressed difference table.

The example memory device 100 can be implemented to include acombination of one or more volatile or nonvolatile computer storagemedia. Computer storage media may be implemented as any suitable methodor technology for storage of information such as computer readableinstructions, data structures, program modules or other data. Apropagating signal by itself does not qualify as storage media or amemory device. The memory device can be included as part of a systemincluding a processor and memory for storing a set of computerinstruction for controlling the processor to perform a colortransformation. Examples include a memory device included as part of aprinter cartridge that can be read by a printer to perform colortransformations based on such specifications such as ink or mediaparameters or device specifications.

FIG. 2 illustrates an example method 200 that can be employed tocompress a color table, or original color table. The examples aredescribed with reference to one-dimensional color tables, i.e., colortables having one input channel, one output channel, and thus M nodes,although the concepts can be transferrable to multi-dimensional colortables and other color profile records. A difference table is compressedat 202. The difference table includes a plurality of difference nodesrepresenting a difference of values of nodes of the color table andnodes of a reference table. The compressed difference table isreconstructed and applied to generate a residue table at 204. Theresidue table includes a plurality of residue nodes representing adifference of values of the nodes of the color table and nodes of areconstructed compressed difference table. The compressed differencetable and residue table can be stored as data files on a memory device,such as device 100.

In one example, the difference color table is compressed at 202 using adiscrete cosine transform, or DCT, which expresses a finite sequence ofdata points in terms of a sum of cosine functions oscillating atdifferent frequencies, although other systems can be employed. DCTcompression can be particularly apt for examples in which color tablesmay be expressed in single or multiple dimensions. In other examples,the difference color table could be compressed using a system that couldbe based on wavelets, such as the SPIHT (Set Partitioning InHierarchical Trees) and SPECK (Set Partitioned Embedded bloCK).

The example method 200 can be implemented to include a combination ofone or more hardware devices and programs for controlling a system, suchas a computing device having a processor and memory, to perform method200 to compress a color table into a file or a bitstream. The file orbitstream may be subdivided into additional files or bitstreams. Method200 can be implemented as a set of executable instructions forcontrolling the processor. Other methods of the disclosure can beimplemented as a combination of hardware and programming for controllinga system as well.

Data compression includes encoding information using fewer bits than theoriginal representation. Lossless compression and lossy compression aretwo forms of data compression. In lossless compression, no digitaldifference exists between the original data and the reconstructedlosslessy compressed data. In contrast, a portion of the original datais lost upon reconstruction of lossy compressed data.

In the example method of 200, a specific lossless compression system canbe employed to exploit particular characteristics of the original colortable to be compressed. The specific lossless compression can be appliedto the original color table into files that can be reconstructed into acolor table with no digital difference from the original color table. Ageneral lossless compression system can be employed to compress any kindof data. One or more of these files can be further compressed with ageneral lossless compression system to further reduce the size of thefiles.

FIG. 3 illustrates an example method 300 of compressing an originalcolor table as in method 200. The example method 300 can be implementedin stages including a specific lossless compression stage that exploitsspecific characteristics of the color table data and a general losslesscompression stage for high data compression. In one example, the stagesof the method are performed consecutively.

Process 300 generates a difference table from the original color tableand a reference table at 302. The difference table includes a pluralityof difference nodes in which each node includes a value that representsa difference of a value of a node of the original color table and avalue of a node of a reference table. In one example, the original colortable and reference table each include M nodes. The value of each nodeof the original color table is subtracted from the value of thecorresponding node in the reference table to provide a value at thecorresponding node in the difference table. Thus, the value at nodelocation j of the original color table is subtracted from the value atnode location j of the reference table to provide the value at nodelocation j of the difference color table, in which j is the nodelocation from 1 to M.

The reference table includes nodes having a preselected, orpredetermined value that may be representative of the nodes of theoriginal color table. In one example, the smaller the values for thedifference nodes, the smaller the values of the nodes in the residuetable, which can provide for efficient compression. In one example,values for reference nodes can be {0, 1, 2 . . . (M−1)} for thereference table.

The difference table is compressed at 304. In the example, thedifference table is compressed via the DCT to generate a set ofcoefficients that can be further processed to generate a set ofquantized coefficients at 306. A difference table having M nodes willgenerate M coefficients. Each of the coefficients in the set ofcoefficients can be divided by, or quantized, with a fixed step size Δand rounded to the nearest integer to provide the set of M quantizedcoefficients at 306. The quantized coefficients can be written to abinary file at 308.

The compressed difference table is reconstructed and applied to thereference table to generate an initially reconstructed table at 310. Forexample, the quantized coefficients from 306 are used to generate areconstructed difference table. In the example, the quantizedcoefficients multiplied by the step size Δ are applied in an inverse DCTprocess and rounded to the nearest integer to obtain the values at thenodes of the reconstructed difference table. The reconstructeddifference table is added to the reference table to obtain the initiallyreconstructed table at 310. In one example, the reconstructed differencetable and reference table each include M nodes, and the value of eachnode of the reconstructed difference table is added to the value at thecorresponding node in the reference table to provide a value at thecorresponding node in the initially reconstructed table.

The initially reconstructed table is subtracted from the original colortable to obtain a residue table at 312. In one example, the initiallyreconstructed table and original table each include M nodes, and thevalue of each node of the initially reconstructed table is subtractedfrom the value of the corresponding node in the original table toprovide a value at the corresponding node in the residue table. Theresidue table can be written to a binary file at 314. In one example,the residue table added to the initially reconstructed table creates acolor table that has no or generally no digital difference from theoriginal color table. In another example the residue table is determinedto that it added to the initially reconstructed table creates anapproximation of the original color table.

The quantized coefficients and residue table are used to calculatecorresponding bit assignment tables. The quantized coefficients are usedto calculate a coefficient bit assignment table (CBAT) at 316 that canbe used to decode the quantized coefficients written to the binary fileat 308. Similarly, the values of the residue table can be used tocalculate a residue bit assignment table (RBAT) at 318 that can be usedto decode the residue table written to the binary file at 314. A singledimensional original color table will include one CBAT and one RBAT.

The CBAT and RBAT generated at 316, 318 store the information related tohow many bits are assigned to each quantized coefficient or residuevalue, respectively. For example, ┌ log₂L┐ bits are used to quantize areal number in the range −0.5 to L−0.5 to an integer value, in which┌log₂(L)┐ represents a ceiling function of the base-2 logarithm of L,log₂(L), and a ceiling function maps the real number to the smallestsubsequent integer. An additional bit is provided for the sign in theCBAT and RBAT because coefficients and residue values can be a negativenumber.

An example process can be applied to calculate a bit assignment tablefor each of the CBAT and RBAT at 316, 318. Fora given output channel,the quantized DCT coefficient of the output channel is denoted asQ_(ij), in which i (from 1 to N) is the color table number and j (from 1to M) is the node number for a single dimensional original color table(and from 1 to M^(J) ^(in) for a multidimensional color table). Thenumber of bits B_(ij) needed for Q_(ij) is B_(i,j)=0 if Q_(ij) is 0 andB_(i,j)=┌log₂|Q_(ij)|┐ if Q_(ij) is not 0.

In one example, a fixed number of bits a can be assigned to every nodeof the respective bit assignment tables and used to determine the sizeof each bit assignment table. The value of the bit assignment tables atnode location j, or L_(j), can be determined from the largest number ofbits B_(i,j) needed for each color table i (from 1 to N). The fixednumber of bits a can be determined from the largest number of┌log₂(L_(j))┐ as determined for each node location j (from 1 to M). Inthe example, the total size of one bit assignment table for a singledimensional color table is thus aM bits.

The total size of the CBAT and RBAT can be significantly reduced via ageneral lossless compression. General lossless compression can beimplemented using a variety of compression systems includingLempel-Ziv-Markov chain Algorithm process (or LZMA), GZIP (or GNU-zip)process, or other suitable lossless compression systems that can beapplied to obtain lossless compression of data files. The CBAT can becompressed at 320 and the RBAT can be compressed at 322 with thelossless compression such as LZMA.

In some examples, the quantized coefficients and residue binary filescan be compressed with the general lossless compression, but LZMA maynot have as good of compression performance for the quantizedcoefficients and residue table as for the bit assignment tables, whichcan include high redundancy.

The selected step size Δ used to generate the quantized coefficients at306 can affect an amount of compression. A compression ratio can bedetermined from the size of the original color table divided by the sizeof the all the files, i.e., the size of the quantized coefficients,residue table, and the bit assignment tables. A larger step size Δachieves smaller quantized DCT coefficients but larger residue values,but a smaller step size Δ achieves larger quantized DCT coefficients butsmaller residue values. An optimized compression ratio balances the sizeof the quantized coefficient file and the size of the residue tablefile. In calculating the compression ratio as a function of step size Δ,it has been determined that the compression ratio first increases,reaches a peak at an optimized step size Δ_(opt), and decreases as stepsize Δ is increased. In one example, a generally high compression ratiocan be achieved at a step size Δ selected of approximately 2.

DCT compression also can be particularly apt for examples in which colortables may be expressed in multiple dimensions. In further processing amultidimensional color table at 306, the J_(in)-dimensional quantizedcoefficients can be reordered into a one-dimensional data stream of aselected order. The selected order can be based upon a multidimensionalzigzag ordering, such as a three-dimensional zigzag ordering, which canbe used to reorder the quantized coefficients because the energy afterthe DCT transform is concentrated in the low frequency domain. Inperforming a three-dimensional ordering, traversals can be configuredsuch that the planes i+j+k=c are visited in increasing order of c and atwo-dimensional zigzagging is performed within each plane. Suchtraversals of the quantized coefficients from low-to-high frequency canintroduce a large amount of redundancy to the coefficient bit assignmenttable, which can provide efficient packing of the data in compression.The resulting one-dimensional data stream of quantized coefficients froma multidimensional color table can be written to a binary file at 308.

In the case of a multidimensional table, each output channel cancorrespond to a separate coefficient bit assignment table. Accordingly,a profile having J_(out) output channels will include J_(out)coefficient bit assignment tables. The nodes in each bit assignmenttable correspond with the nodes of the original color table.

FIG. 4 illustrates an example memory device 400 including the compressedcolor table 402, which can correspond with compressed color table 102 ofFIG. 1. The compressed color table 402 stored on the memory device 400includes bitstreams of quantized coefficients 404, a compressedcoefficient bit assignment table (CBAT) 406, a residue table 408, and acompressed residue bit assignment table (RBAT) 410. For example, abitstream of the quantized coefficients 404 can be determined frommethod 300 at 308, a bitstream of the compressed CBAT 406 determined at320, a bitstream of the residue table 408 determined at 312, and abitstream of the compressed RBAT 410 determined at 322, which are storedon the memory device 400. In one example, the CBAT and RBAT arecompressed with an LZMA process and compressed CBAT 406 and compressedRBAT 410 are stored as .lzma files on memory device 400. In one example,the quantized coefficients 404 and residue table 408 are stored as abinary file (.bin) on memory device 400. (In another example, thequantized coefficients and residue tables generated at 308, 312 arecompressed with a general compression technique such as LZMA and files404 and 408 are stored on memory device 400 as .lmza files.) Memorydevice 400 can be an example of memory device 100.

FIG. 5 illustrates an example method 500 of decoding the compressedoriginal color table 402, such as the files 404-410 on memory device400.

If one or more files 402, 404, 406, or 408 are compressed with a generallossless compression, the standard losslessly compressed files 402, 404,406, or 408 on memory device 400 are decompressed at 502. For example, astandard lossless decompression technique, such as inverse LZMA orinverse GZIP (i.e., the inverse of the general lossless compressionapplied at 320, 322 and to other files) is applied to the compressedCBAT and RBAT files 406, 410 to yield the decompressed bit assignmenttables, or CBAT and RBAT, at 502.

The decompressed CBAT is used to reconstruct the quantized coefficients,and the decompressed RBAT is used to reconstruct the residue table at504. For example, the decompressed CBAT is applied to the quantizedcoefficient file 404 to determine how many bits of the binary stream areassigned to each quantized coefficient value of the M coefficients.Similarly, the decompressed RBAT is applied to the residue table file408 to determine how many bits of the binary stream are assigned to eachnode of the residue table.

The set of M reconstructed quantized coefficients from 504 are processedto obtain the difference table at 506. The reconstructed coefficientsare multiplied by the quantized step size Δ to obtain preprocessedcoefficients. If a DCT was used to determine the coefficients at 304, aninverse DCT process is applied to the preprocessed coefficients androunded to the nearest integer to obtain M nodes in a decompresseddifference table at 506.

The reference table used at 302 is added to the decompressed differencetable from 506 to obtain an intermediate table at 508. In one example,the decompressed difference table and reference table each include Mnodes, and the value of each node of the decompressed difference tableis added to the value of the corresponding node in the reference tableto provide a value at the corresponding node in the intermediate table.Thus, the value at node location j of the decompressed difference tableis added to the value at node location j of the reference table toprovide the value at node location j of the intermediate table, in whichj is the node location from 1 to M.

The intermediate table from 508 is added to the reconstructed residuetable from 504 to obtain a decompressed original color table at 510. Inone example, the intermediate table and reconstructed residue table eachinclude M nodes, and the value of each node of the intermediate table isadded to the value of the corresponding node in the reconstructedresidue table to provide a value at the corresponding node in thedecompressed original color table. Thus, the value at node location j ofthe intermediate table is added to the value at node location j of thereconstructed residue table to provide the value at node location j ofthe decompressed original color table, in which j is the node locationfrom 1 to M. The decompressed original color table is the same as theoriginal color table compressed with method 300.

The methods of compressing a single dimensional color table, such asmethod 300, were applied to 1DX1_75percent_nonlinear_mono.cxf and1DX1_90percent_nonlinear_mono.cxf tables using a 1DX1_unity.cxf as areference table. The reference table includes 256 nodes, which includesnode increasing linearly from 0 to 255. The reference table can bestored on memory device 100, but also can be readily calculated and isnot stored as part of the files of the compressed original color table.In this example, the M=256 and the bytedepth (the number of bytes usedto store the value in each node) is b=2. In total, there are bM=256bytes in each table and a total of 512 bytes in both tables. An integerstep size Δ of 2 was selected to relatively optimize the balance of thesize of the residue values and the size of the coefficients.

The residue table, quantized coefficients, RBAT, and CBAT were writtenas .bin binary files and compressed with a general lossless LZMAcompression to become .lzma files. The residue table and quantizedcoefficients were not further compressed with a general losslesscompression because the .lzma files were determined to be larger in sizethan the corresponding .bin files. Accordingly, the residue table andthe quantized coefficients were stored as binary files while the RBATand CBAT were stored as .lzma files.

Table 1 shows the size of the files in bytes when the residue table andquantized coefficients were stored as binary files and the RBAT and CBATwere stored as .lzma files. The two compressed original color tablesoccupied only 168 bytes, as compared to 512 bytes for the originaltables, for a compression ratio of 3.05.

TABLE 1 Compressed File Size in Bytes Residue Table 35 RBAT 76 QuantizedDCT Coefficients 23 CBAT 34 Total Size 168

FIG. 6 illustrates an example system 600 that can be used to create acompressed color table 602 on a memory device 604. The compressed colortable 602 can include a compressed difference table 616 and residuetable 618. In one example, memory device 604 can correspond with one ofthe example memory devices 100, 400. For example, the compressed colortable 602 can include the bitstreams of quantized coefficients 404, acompressed coefficient bit assignment table (CBAT) 406, a residue table408, and a compressed residue bit assignment table (RBAT) 410 ofcompressed color table 402. Example system 600 includes a computingdevice 606 having a processor 608 and memory 610 that are configured toimplement an example method of this disclosure, such as one or more ofmethods 200, 300 as a set of computer readable instructions stored inmemory 610 for controlling the processor 608 to perform the method. Inone example, the set of computer readable instructions can beimplemented as a computer program 612 that can include variouscombinations of hardware and programming configured to operate oncomputing device 606. Computer program 612 can be stored in memory 610and executed by the processor 608 to create the compressed color table602 on memory device 604. The memory device 604 can be included in aconsumable product 614 such as a printer cartridge.

FIG. 7 illustrates an example system 700 that can be used to apply thecompressed color table 602 created on memory device 604 with a system,such as system 600. In the example, the memory device 604 is included inthe consumable product 614 such as a printer cartridge having areservoir of liquid ink, dry toner powder, or other printing or markingsubstance for use with a printer. In one example, the printer cartridgeincludes a color table corresponding with the printing or markingsubstance, such as a color table corresponding to black, cyan, magenta,or yellow ink.

The memory device 604 can be operably coupled to another computingdevice 702 having a processor 704 and memory 706 to read and apply thecompressed color table 602. In one example, computing device 702includes inherent printing capability and may be configured as a laserprinter or ink-jet printer that can accept the memory device 604 anddecompress and read the compressed color table 602 as a color look uptable. The computing device 702 can include a set of computer readableinstructions stored in memory 706 and executable by processor 704 toperform a method, such as the method 500 to decompress the color table602 or otherwise apply the color table 602. In one example, the set ofcomputer readable instructions can be implemented as a computer program708 that can include various combinations of hardware and programmingconfigured to operate on computing device 702. Computer program 708 canbe stored in memory 706 and executed by the processor 704 to decompressthe compressed color table 602 on memory device 604. In one example, thememory 706 can store the reference table used method 500. In anotherexample, the reference table can be included as part of computer program708 such as a data in data structure or as created with computer programvia calculations performed with processor 704 and stored in memory 706.

In one example, the computing device 702 is coupled to a computernetwork such as the internet, and the compressed color table 602 isstored on a memory device 604 coupled to the computing device 702 viathe network. The consumable product may include a code that, whenactivated with the computing device 702, the computing device downloadsthe compressed color table 602 (and also possibly the reference table)from the memory device to the memory 706 to read and apply thecompressed color table 602 with the processor 704.

Although specific examples have been illustrated and described herein, avariety of alternate and/or equivalent implementations may besubstituted for the specific examples shown and described withoutdeparting from the scope of the present disclosure. This application isintended to cover any adaptations or variations of the specific examplesdiscussed herein. Therefore, it is intended that this disclosure belimited only by the claims and the equivalents thereof.

The invention claimed is:
 1. A print cartridge comprising: a memorydevice comprising: quantized coefficients derived from a compression ofa difference table including a plurality of difference nodes in whicheach difference node represents a value that is a difference of a valueof a node of a color table and a value of a corresponding node of areference table, the quantized coefficients useable to produce areconstructed difference table; and a plurality of residue nodes inwhich each residue node represents a value that is a difference of avalue of a node of the color table and a value of a corresponding nodeof the reconstructed difference table, wherein the quantizedcoefficients and the plurality of residue nodes are accessible by aprinting device to reconstruct a color table and perform a colortransformation between color spaces when printing.
 2. The printcartridge of claim 1, wherein the memory device comprises a residuetable that includes the plurality of residue nodes.
 3. The printcartridge of claim 2, wherein the memory device comprises a residue bitassignment table useable to decode the residue table.
 4. The printcartridge of claim 3, wherein the residue bit assignment table indicateshow many bits are assigned to each residue node of the plurality ofresidue nodes.
 5. The print cartridge of claim 1, wherein the quantizedcoefficients are based on coefficients derived from application of adiscrete cosine transform on the difference table.
 6. The printcartridge of claim 1, wherein the quantized coefficients comprise a datastream of quantized coefficients.
 7. The print cartridge of claim 6,wherein the data stream of quantized coefficients is a one-dimensionaldata stream of quantized coefficients.
 8. The print cartridge of claim1, wherein the memory device comprises a compressed version of thequantized coefficients and the plurality of residue nodes, thecompressed version derived from lossless compression of the quantizedcoefficients and the plurality of residue nodes.
 9. The print cartridgeof claim 8, wherein the quantized coefficients are useable to producethe reconstructed difference table based on inverting the compression.10. The print cartridge of claim 1, wherein the memory device furthercomprises a coefficient bit assignment table that includes informationrelated to a number of bits assigned to each of the quantizedcoefficients.
 11. The print cartridge of claim 1, wherein the memorydevice comprises a bitstream of the quantized coefficients, a bitstreamof a coefficient bit assignment table, a bitstream of the plurality ofresidue nodes, and a bitstream of a residue bit assignment table. 12.The print cartridge of claim 11, wherein the bitstreams of thecoefficient bit assignment table and the residue bit assignment tableare compressed with a lossless compression.
 13. The print cartridge ofclaim 1, further comprising a print material reservoir storing a printmaterial.
 14. The print cartridge of claim 1, further comprising areservoir storing black ink or toner.
 15. The print cartridge of claim1, wherein the quantized coefficients are derived from a lossycompression of the difference table.
 16. A print cartridge, comprising:a memory device comprising: quantized coefficients derived from acompression of a difference table including a plurality of differencenodes in which each difference node represents a value that is adifference of a value of a node of a color table and a value of acorresponding node of a reference table, the quantized coefficientsuseable to produce a reconstructed difference table; and a residue tableincluding a plurality of residue nodes in which each residue noderepresents a value that is a difference of a value of a node of thecolor table and a value of a corresponding node of the reconstructeddifference table, wherein the quantized coefficients and the pluralityof residue nodes are accessible by a printing device to reconstruct acolor table and perform a color transformation between color spaces whenprinting.
 17. The print cartridge of claim 16, wherein the memory devicefurther comprises a coefficient bit assignment table useable to decodethe quantized coefficients, the coefficient bit assignment tableincluding information related to a number of bits assigned to each ofthe quantized coefficients.
 18. The print cartridge of claim 16, whereinthe memory device further comprises a residue bit assignment tableuseable to decode the residue table, the residue bit assignment tableindicating how many bits are assigned to each residue node of theresidue table.
 19. The print cartridge of claim 16, further comprising areservoir of black toner or ink, and wherein the color table is amonochromatic color table.
 20. The print cartridge of claim 16, whereinthe quantized coefficients are useable with the reference table on aprinting device to provide the reconstructed difference table.
 21. Aprint cartridge comprising: a memory device comprising a compressed datastructure to construct a one-dimensional color transformation table fora printer, the data structure comprising: quantized coefficients derivedfrom a compression of a difference table including a plurality ofdifference nodes in which each difference node represents a value thatis to be combined with a corresponding node of a reference table, thequantized coefficients useable to produce a reconstructed differencetable; a residue table including a plurality of residue nodes in whicheach residue node is to be combined with a corresponding node of thecombination of the reconstructed difference table and the referencetable; and a residue bit assignment table useable to decode the residuetable, the residue bit assignment table indicating how many bits areassigned to each residue node of the residue table, wherein thequantized coefficients and the plurality of residue nodes are accessibleby the printer to reconstruct a color table and perform a colortransformation between color spaces when printing.
 22. The printcartridge of claim 21, wherein the compressed data structure is alosslessly compressed data structure.
 23. The print cartridge of claim22, wherein the lossless compression is a Lempel-Ziv-Markov chainAlgorithm compression.
 24. The print cartridge of claim 21, wherein thequantized coefficients are derived from a lossy compression of thedifference table.
 25. The print cartridge of claim 21, wherein thequantized coefficients are quantized with a fixed step size using thelossy compression.
 26. The print cartridge of claim 21, wherein thequantized coefficients are to be reconstructed using a cosine bitassignment table stored on the printer or cartridge, and multiplied by afixed step size to obtain the decompressed difference table.
 27. Theprint cartridge of claim 21, wherein the compressed data structurefurther comprises a coefficient bit assignment table derived from thequantized coefficients, the coefficient bit assignment table useable todecode the quantized coefficients, the coefficient bit assignment tableincluding information related to a number of bits assigned to each ofthe quantized coefficients.
 28. The print cartridge of claim 21, whereinthe residue bit assignment table is derived from the residue table. 29.The print cartridge of claim 21, comprising black print material.